1. Field of the Invention
The present invention relates to a technology for compensating for the variation of the Q value of a filter circuit.
2. Description of the Related Art
Recently, the LSI embedding of an active RC type filter has been promoted. In order to obtain stable characteristics from a filter circuit, a technology disclosed by Patent reference 1 is proposed. For example, in order to obtain a filter characteristic with a steep Q value, a circuit design in which a Q value has a negative temperature characteristic and the gain of a circuit before or after the filter circuit has a negative temperature characteristic is proposed.
Although a filter circuit includes a plurality of methods, the bi-quad filter is widely used.
In FIG. 1, a bi-quad filter (variable-capacitance type) is a two-pole filter.
VIP1 and VIN2 are input terminals to which differential input signals are input. OUTM3 and OUTP4 are output terminals from which differential output signals are output. Reference numerals 5-12 are resistive elements. Reference numerals 17 and 18 are differential operational amplifiers, and reference numerals 13-16 are capacitive elements. A cut-off frequency is adjusted by changing the capacitance value of the capacitive elements.
In the above-mentioned bi-quad filter, a resistive element 5 is connected to its input terminal 1 (VIP), and the other terminal of the resistance 5 is connected to the inverted input (−) of the differential operational amplifier 17. The resistive element 6 is connected to the input terminal 2 (VIN), and the other terminal of the resistive element 6 is connected to the non-inverted input (+) of the differential operational amplifier 17.
The resistive elements 8 and 12, and one terminal of the capacitive element 14 are connected to the non-inverted input (+) of the differential operational amplifier 17, and the other terminal of the resistive element 12 is connected to the non-inverted output (+) of the differential operational amplifier 18, and the resistive element 8 and the other terminal of the capacitive element 14 is connected to the inverted output (−) of the differential output (−) of the differential operational amplifier 17.
One output terminal (+) of the operational amplifier 17 is connected to the output terminal 3 (OUTM), and the other output terminal (−) is connected to the output terminal 4 (OUTP).
One terminal of the resistive element 9 is connected to the non-inverted output (+) of the differential operational amplifier 17, and the other terminal of the resistive element 9 is connected to the inverted input (−) of the differential operational amplifier 18. One end of the resistive elements 10 is connected to the inverted output (−) of the differential operation amplifier 17, and the other terminal of the resistive element 10 is connected to the non-inverted input (+) of the differential operational amplifier 18.
One terminal of the capacitive element 15 is connected to the inverted input (−) of the differential operational amplifier 18, and the other terminal is connected to the non-inverted output (+) of the differential operation amplifier 18. One terminal of the capacitive element 16 is connected to the non-inverted input (+) of the differential operational amplifier 18, and the other terminal is connected to the inverted output (−) of the differential operational amplifier 18.
Equation (1) indicates the general form of the transmission function of a band-pass filter composed of the above-mentioned bi-quad filter.
                    [                  Mathematical          ⁢                                          ⁢          expression          ⁢                                          ⁢          1                ]                                                            Ts        =                              K            ⁢                                          w                ⁢                                                                  ⁢                1                            Q                        ⁢            s                                              s              2                        +                                                            w                  ⁢                                                                          ⁢                  1                                Q                            ⁢              s                        +                          w              ⁢                                                          ⁢                              1                2                                                                        (        1        )            
FIG. 2 shows the frequency characteristic of a band-pass filter described by the transmission function. FIG. 2 shows the ideal frequency characteristic in the case where there are no influences of the DC gain or unity gain angular frequency of the operational amplifier.
In FIG. 2, w1 and BW represent the center angular frequency of a band-pass filter and the frequency bandwidth, respectively. The Q value can be obtained by w1/BW.
In this case, a cut-off frequency (time constant) is inversely proportional to the resistance×capacitance, and fluctuates due to the influences of the resistive element in the LSI, the variation of the capacitive element at the time of manufacturing, temperature change at the time of operation and the like. In order to suppress this fluctuation, a resistance value or a capacitance value is made variable, and it is adjusted in such a way that the cut-off frequency can be kept constant, by an automatic adjustment circuit or manually.
The frequency characteristics of a filter, such as gain ripple, group delay ripple and the like, are affected by the frequency characteristics of the operational amplifier (such as DC gain and unity gain). The frequency characteristics of the operational amplifier (such as DC gain and unity gain) are affected by variation at the time of manufacturing, temperature fluctuation and the like including those inside the LSI. Therefore, the Q value of a filter varies and a filters shape (such as its gain ripple and group delay ripple) varies.
In the case of a bi-quad filter, the relationship between the Q value and the frequency characteristic of an operational amplifier can be approximately expressed by equation (2).
                    [                  Mathematical          ⁢                                          ⁢          expression          ⁢                                          ⁢          2                ]                                                            Qef        =                  Q                      1            -                          2              ⁢                              Q                ⁡                                  (                                                            wc                      wo                                        -                                          1                                              A                        ⁢                                                                                                  ⁢                        0                                                                              )                                                                                        (        2        )            
Qef: Actual Q value
wc: Cut-off angular frequency of a filter
Q: Design value
wo: Unity gain angular frequency of an operational amplifier
A0: DC gain of an operational amplifier
According to equation (2), if wo or A0 changes, Qef changes. Therefore, generally, in order to suppress the fluctuation of a Q value, a method for sufficiently increasing the DC gain (A0) and unity gain angular frequency (wo) of an operational amplifier is proposed.
However, generally, although DC gain can be sufficiently increased, unity gain angular frequency (wo) cannot be increased sufficiently. That is because if the unity gain angular frequency (wo) of an operational amplifier is increased in order to suppress the fluctuation of a Q value, the power consumption of a high-speed operational amplifier tends to increase, which is not suitable for low power consumption. Even the high-speed of an operational amplifier is limited, which is a problem. Therefore, it is difficult to manufacture a filter with a small Q value fluctuation, whose gain ripple and group delay ripple are stable, with low power consumption.
Although Patent reference 1 discloses a method for eliminating the temperature fluctuation of a Q value, due to the frequency temperature characteristic of a transistor and eliminating the temperature fluctuation of gain, due to the fluctuation of the Q value, it does not disclose a method for stabilizing gain ripple and group delay ripple.
Patent reference 1: Japanese Patent Application No. H5-259808